In-class_Exercise 5: Modeling the Spatial Variantion: the Explanatory Factors of Water Point Status using Geograhical Weighted Logistic Regression

Setting the scene

To build an explanatory model to discover factor affecting water point status in Osun State, Nigeria.

Study Area: Osun State, Nigeria

Data Sets:

  • Osun.rds contains LGA boundaries of Osun State. It is in sf polygon data frame.

  • Osun_wp_sf.rds: contains water points within Osun State. It is in sf point data frame.

Model Variables

Dependent variable: Water point status (i.e functional/non-functoinal)

Independent variables:

  • distance_to_primary_road,

  • distance_ to_secondary_road,

  • distance_to_tertiary_road,

  • distance_to_city,

  • distance_to_town,

  • water_point_population,

  • local_population_km,

  • usage_capacity,

  • is_urban,

  • water_source_clean.

R packages

The code chunk below is used to load the packages to R environment.

pacman::p_load(tidyverse, funModeling, blorr, corrplot, ggpubr, sf,
               spdep, GWmodel, tmap, skimr, caret, report)

The Data

The code chunk below is used to load the data to R environment.

Osun <- read_rds("rds/Osun.rds")
Osun_wp_sf <- read_rds("rds/Osun_wp_sf.rds")

The code chunk below is used to show the frequency distribution of water point status.

True refers to Functional water points while False refers to non-functional water points.

Osun_wp_sf %>%
  freq(input="status")
Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
  Please report the issue at <https://github.com/pablo14/funModeling/issues>.

  status frequency percentage cumulative_perc
1   TRUE      2642       55.5            55.5
2  FALSE      2118       44.5           100.0
tmap_mode("view")
tmap mode set to interactive viewing
tm_shape(Osun)+
  tm_polygons(alpha = 0.4) +
tm_shape(Osun_wp_sf) +
  tm_dots(col="status",
          alpha = 0.6) +
  tm_view(set.zoom.limits = c(9,12))

Exploratory Data Analysis(EDA)

The code chunk below is used to do EDA for all variables.

Osun_wp_sf %>%
  skim()
Warning: Couldn't find skimmers for class: sfc_POINT, sfc; No user-defined `sfl`
provided. Falling back to `character`.
Data summary
Name Piped data
Number of rows 4760
Number of columns 75
_______________________
Column type frequency:
character 47
logical 5
numeric 23
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
source 0 1.00 5 44 0 2 0
report_date 0 1.00 22 22 0 42 0
status_id 0 1.00 2 7 0 3 0
water_source_clean 0 1.00 8 22 0 3 0
water_source_category 0 1.00 4 6 0 2 0
water_tech_clean 24 0.99 9 23 0 3 0
water_tech_category 24 0.99 9 15 0 2 0
facility_type 0 1.00 8 8 0 1 0
clean_country_name 0 1.00 7 7 0 1 0
clean_adm1 0 1.00 3 5 0 5 0
clean_adm2 0 1.00 3 14 0 35 0
clean_adm3 4760 0.00 NA NA 0 0 0
clean_adm4 4760 0.00 NA NA 0 0 0
installer 4760 0.00 NA NA 0 0 0
management_clean 1573 0.67 5 37 0 7 0
status_clean 0 1.00 9 32 0 7 0
pay 0 1.00 2 39 0 7 0
fecal_coliform_presence 4760 0.00 NA NA 0 0 0
subjective_quality 0 1.00 18 20 0 4 0
activity_id 4757 0.00 36 36 0 3 0
scheme_id 4760 0.00 NA NA 0 0 0
wpdx_id 0 1.00 12 12 0 4760 0
notes 0 1.00 2 96 0 3502 0
orig_lnk 4757 0.00 84 84 0 1 0
photo_lnk 41 0.99 84 84 0 4719 0
country_id 0 1.00 2 2 0 1 0
data_lnk 0 1.00 79 96 0 2 0
water_point_history 0 1.00 142 834 0 4750 0
clean_country_id 0 1.00 3 3 0 1 0
country_name 0 1.00 7 7 0 1 0
water_source 0 1.00 8 30 0 4 0
water_tech 0 1.00 5 37 0 20 0
adm2 0 1.00 3 14 0 33 0
adm3 4760 0.00 NA NA 0 0 0
management 1573 0.67 5 47 0 7 0
adm1 0 1.00 4 5 0 4 0
New Georeferenced Column 0 1.00 16 35 0 4760 0
lat_lon_deg 0 1.00 13 32 0 4760 0
public_data_source 0 1.00 84 102 0 2 0
converted 0 1.00 53 53 0 1 0
created_timestamp 0 1.00 22 22 0 2 0
updated_timestamp 0 1.00 22 22 0 2 0
Geometry 0 1.00 33 37 0 4760 0
ADM2_EN 0 1.00 3 14 0 30 0
ADM2_PCODE 0 1.00 8 8 0 30 0
ADM1_EN 0 1.00 4 4 0 1 0
ADM1_PCODE 0 1.00 5 5 0 1 0

Variable type: logical

skim_variable n_missing complete_rate mean count
rehab_year 4760 0 NaN :
rehabilitator 4760 0 NaN :
is_urban 0 1 0.39 FAL: 2884, TRU: 1876
latest_record 0 1 1.00 TRU: 4760
status 0 1 0.56 TRU: 2642, FAL: 2118

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
row_id 0 1.00 68550.48 10216.94 49601.00 66874.75 68244.50 69562.25 471319.00 ▇▁▁▁▁
lat_deg 0 1.00 7.68 0.22 7.06 7.51 7.71 7.88 8.06 ▁▂▇▇▇
lon_deg 0 1.00 4.54 0.21 4.08 4.36 4.56 4.71 5.06 ▃▆▇▇▂
install_year 1144 0.76 2008.63 6.04 1917.00 2006.00 2010.00 2013.00 2015.00 ▁▁▁▁▇
fecal_coliform_value 4760 0.00 NaN NA NA NA NA NA NA
distance_to_primary_road 0 1.00 5021.53 5648.34 0.01 719.36 2972.78 7314.73 26909.86 ▇▂▁▁▁
distance_to_secondary_road 0 1.00 3750.47 3938.63 0.15 460.90 2554.25 5791.94 19559.48 ▇▃▁▁▁
distance_to_tertiary_road 0 1.00 1259.28 1680.04 0.02 121.25 521.77 1834.42 10966.27 ▇▂▁▁▁
distance_to_city 0 1.00 16663.99 10960.82 53.05 7930.75 15030.41 24255.75 47934.34 ▇▇▆▃▁
distance_to_town 0 1.00 16726.59 12452.65 30.00 6876.92 12204.53 27739.46 44020.64 ▇▅▃▃▂
rehab_priority 2654 0.44 489.33 1658.81 0.00 7.00 91.50 376.25 29697.00 ▇▁▁▁▁
water_point_population 4 1.00 513.58 1458.92 0.00 14.00 119.00 433.25 29697.00 ▇▁▁▁▁
local_population_1km 4 1.00 2727.16 4189.46 0.00 176.00 1032.00 3717.00 36118.00 ▇▁▁▁▁
crucialness_score 798 0.83 0.26 0.28 0.00 0.07 0.15 0.35 1.00 ▇▃▁▁▁
pressure_score 798 0.83 1.46 4.16 0.00 0.12 0.41 1.24 93.69 ▇▁▁▁▁
usage_capacity 0 1.00 560.74 338.46 300.00 300.00 300.00 1000.00 1000.00 ▇▁▁▁▅
days_since_report 0 1.00 2692.69 41.92 1483.00 2688.00 2693.00 2700.00 4645.00 ▁▇▁▁▁
staleness_score 0 1.00 42.80 0.58 23.13 42.70 42.79 42.86 62.66 ▁▁▇▁▁
location_id 0 1.00 235865.49 6657.60 23741.00 230638.75 236199.50 240061.25 267454.00 ▁▁▁▁▇
cluster_size 0 1.00 1.05 0.25 1.00 1.00 1.00 1.00 4.00 ▇▁▁▁▁
lat_deg_original 4760 0.00 NaN NA NA NA NA NA NA
lon_deg_original 4760 0.00 NaN NA NA NA NA NA NA
count 0 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00 ▁▁▇▁▁
Osun_wp_sf_clean <- Osun_wp_sf %>%
  filter_at(vars(status,
                 distance_to_primary_road,
                 distance_to_secondary_road,
                 distance_to_tertiary_road,
                 distance_to_city,
                 distance_to_town,
                 water_point_population,
                 local_population_1km,
                 usage_capacity,
                 is_urban,
                 water_source_clean),
            all_vars(!is.na(.))) %>%
    mutate(usage_capacity = as.factor(usage_capacity))

The code chunk below is used to drop away geometric column

Osun_wp <- Osun_wp_sf_clean %>%
  select(c(7,35:39,42:43,46:47,57)) %>%
  st_set_geometry(NULL)
cluster_vars.cor = cor(
  Osun_wp[,2:7])
corrplot.mixed(cluster_vars.cor,
               lower = "ellipse",
               upper = "number",
               tl.pos = "lt",
               diag = "l",
               tl.col = "black")

model <- glm(status ~ distance_to_primary_road +
                distance_to_secondary_road +
                 distance_to_tertiary_road +
                 distance_to_city +
                 distance_to_town +
                 water_point_population +
                 local_population_1km +
                 usage_capacity +
                 is_urban +
                 water_source_clean,
        data = Osun_wp_sf_clean,
        family = binomial(link = "logit"))

Instead of using typical R project, blr_regress() of blorr package is used.

blr_regress(model)
                             Model Overview                              
------------------------------------------------------------------------
Data Set    Resp Var    Obs.    Df. Model    Df. Residual    Convergence 
------------------------------------------------------------------------
  data       status     4756      4755           4744           TRUE     
------------------------------------------------------------------------

                    Response Summary                     
--------------------------------------------------------
Outcome        Frequency        Outcome        Frequency 
--------------------------------------------------------
   0             2114              1             2642    
--------------------------------------------------------

                                 Maximum Likelihood Estimates                                   
-----------------------------------------------------------------------------------------------
               Parameter                    DF    Estimate    Std. Error    z value     Pr(>|z|) 
-----------------------------------------------------------------------------------------------
              (Intercept)                   1      0.3887        0.1124      3.4588       5e-04 
        distance_to_primary_road            1      0.0000        0.0000     -0.7153      0.4744 
       distance_to_secondary_road           1      0.0000        0.0000     -0.5530      0.5802 
       distance_to_tertiary_road            1      1e-04         0.0000      4.6708      0.0000 
            distance_to_city                1      0.0000        0.0000     -4.7574      0.0000 
            distance_to_town                1      0.0000        0.0000     -4.9170      0.0000 
         water_point_population             1      -5e-04        0.0000    -11.3686      0.0000 
          local_population_1km              1      3e-04         0.0000     19.2953      0.0000 
           usage_capacity1000               1     -0.6230        0.0697     -8.9366      0.0000 
              is_urbanTRUE                  1     -0.2971        0.0819     -3.6294       3e-04 
water_source_cleanProtected Shallow Well    1      0.5040        0.0857      5.8783      0.0000 
   water_source_cleanProtected Spring       1      1.2882        0.4388      2.9359      0.0033 
-----------------------------------------------------------------------------------------------

 Association of Predicted Probabilities and Observed Responses  
---------------------------------------------------------------
% Concordant          0.7347          Somers' D        0.4693   
% Discordant          0.2653          Gamma            0.4693   
% Tied                0.0000          Tau-a            0.2318   
Pairs                5585188          c                0.7347   
---------------------------------------------------------------
report(model)
We fitted a logistic model (estimated using ML) to predict status with
distance_to_primary_road (formula: status ~ distance_to_primary_road +
distance_to_secondary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + water_point_population + local_population_1km +
usage_capacity + is_urban + water_source_clean). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
distance_to_primary_road = 0, is at 0.39 (95% CI [0.17, 0.61], p < .001).
Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_secondary_road
(formula: status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_secondary_road = 0,
is at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_tertiary_road (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_tertiary_road = 0,
is at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_city (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_city = 0, is at 0.39
(95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_town (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_town = 0, is at 0.39
(95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with water_point_population (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to water_point_population = 0, is
at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with local_population_1km (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to local_population_1km = 0, is at
0.39 (95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with usage_capacity (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to usage_capacity = 300, is at 0.39
(95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with is_urban (formula: status ~
distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to is_urban = [?], is at 0.39 (95%
CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation. and We fitted a logistic
model (estimated using ML) to predict status with water_source_clean (formula:
status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
water_point_population + local_population_1km + usage_capacity + is_urban +
water_source_clean). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to water_source_clean = Borehole,
is at 0.39 (95% CI [0.17, 0.61], p < .001). Within this model:

  - The effect of distance to primary road is statistically non-significant and
negative (beta = -4.64e-06, 95% CI [-1.74e-05, 8.07e-06], p = 0.474; Std. beta
= -0.03, 95% CI [-0.10, 0.05])
  - The effect of distance to secondary road is statistically non-significant and
negative (beta = -5.14e-06, 95% CI [-2.34e-05, 1.31e-05], p = 0.580; Std. beta
= -0.02, 95% CI [-0.09, 0.05])
  - The effect of distance to tertiary road is statistically significant and
positive (beta = 9.68e-05, 95% CI [5.64e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.09, 0.23])
  - The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.92e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of distance to town is statistically significant and negative
(beta = -1.48e-05, 95% CI [-2.07e-05, -8.91e-06], p < .001; Std. beta = -0.18,
95% CI [-0.26, -0.11])
  - The effect of water point population is statistically significant and
negative (beta = -5.10e-04, 95% CI [-6.01e-04, -4.26e-04], p < .001; Std. beta
= -0.74, 95% CI [-0.88, -0.62])
  - The effect of local population 1km is statistically significant and positive
(beta = 3.45e-04, 95% CI [3.11e-04, 3.81e-04], p < .001; Std. beta = 1.45, 95%
CI [1.30, 1.60])
  - The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
  - The effect of is urbanTRUE is statistically significant and negative (beta =
-0.30, 95% CI [-0.46, -0.14], p < .001; Std. beta = -0.30, 95% CI [-0.46,
-0.14])
  - The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.34, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.34, 0.67])
  - The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.48, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.48, 2.23])

Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation.
blr_confusion_matrix(model, cutoff = 0.5)
Confusion Matrix and Statistics 

          Reference
Prediction FALSE TRUE
         0  1301  738
         1   813 1904

                Accuracy : 0.6739 
     No Information Rate : 0.4445 

                   Kappa : 0.3373 

McNemars's Test P-Value  : 0.0602 

             Sensitivity : 0.7207 
             Specificity : 0.6154 
          Pos Pred Value : 0.7008 
          Neg Pred Value : 0.6381 
              Prevalence : 0.5555 
          Detection Rate : 0.4003 
    Detection Prevalence : 0.5713 
       Balanced Accuracy : 0.6680 
               Precision : 0.7008 
                  Recall : 0.7207 

        'Positive' Class : 1
Osun_wp_sp <- Osun_wp_sf_clean %>%
  select(c(status,
                 distance_to_primary_road,
                 distance_to_secondary_road,
                 distance_to_tertiary_road,
                 distance_to_city,
                 distance_to_town,
                 water_point_population,
                 local_population_1km,
                 usage_capacity,
                 is_urban,
                 water_source_clean)) %>%
  as_Spatial()
Osun_wp_sp
class       : SpatialPointsDataFrame 
features    : 4756 
extent      : 182502.4, 290751, 340054.1, 450905.3  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs 
variables   : 11
names       : status, distance_to_primary_road, distance_to_secondary_road, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean 
min values  :      0,        0.014461356813335,          0.152195902540837,         0.017815121653488, 53.0461399623541, 30.0019777713073,                      0,                    0,           1000,        0,           Borehole 
max values  :      1,         26909.8616132094,           19559.4793799085,          10966.2705628969,  47934.343603562, 44020.6393368124,                  29697,                36118,            300,        1,   Protected Spring 
bw.fixed <- bw.ggwr(status ~
                      distance_to_primary_road +
                 distance_to_secondary_road +
                 distance_to_tertiary_road +
                 distance_to_city +
                 distance_to_town +
                 water_point_population +
                 local_population_1km +
                 usage_capacity +
                 is_urban +
                 water_source_clean,
                 data = Osun_wp_sp,
                 family = "binomial",
                 approach = "AIC",
                 kernel = "gaussian",
                 adaptive = FALSE,
                 longlat = FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
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       5        -1339 
Fixed bandwidth: 2479.775 AICc value: 4764.294 
 Iteration    Log-Likelihood:(With bandwidth:  2593.343 )
=========================
       0        -1956 
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Fixed bandwidth: 2593.343 AICc value: 4761.813 
 Iteration    Log-Likelihood:(With bandwidth:  2620.153 )
=========================
       0        -1965 
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Fixed bandwidth: 2620.153 AICc value: 4761.89 
 Iteration    Log-Likelihood:(With bandwidth:  2576.774 )
=========================
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Fixed bandwidth: 2576.774 AICc value: 4761.889 
 Iteration    Log-Likelihood:(With bandwidth:  2603.584 )
=========================
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Fixed bandwidth: 2603.584 AICc value: 4761.813 
 Iteration    Log-Likelihood:(With bandwidth:  2609.913 )
=========================
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Fixed bandwidth: 2609.913 AICc value: 4761.831 
 Iteration    Log-Likelihood:(With bandwidth:  2599.672 )
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Fixed bandwidth: 2599.672 AICc value: 4761.809 
 Iteration    Log-Likelihood:(With bandwidth:  2597.255 )
=========================
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Fixed bandwidth: 2597.255 AICc value: 4761.809 
bw.fixed
[1] 2599.672
gwlr.fixed <- ggwr.basic(status ~
                      distance_to_primary_road +
                 distance_to_secondary_road +
                 distance_to_tertiary_road +
                 distance_to_city +
                 distance_to_town +
                 water_point_population +
                 local_population_1km +
                 usage_capacity +
                 is_urban +
                 water_source_clean,
                 data = Osun_wp_sp,
                 bw = 2597.255,
                 family="binomial",
                 kernel = "gaussian",
                 adaptive = FALSE,
                 longlat = FALSE)
 Iteration    Log-Likelihood
=========================
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gwlr.fixed
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2022-12-17 11:42:45 
   Call:
   ggwr.basic(formula = status ~ distance_to_primary_road + distance_to_secondary_road + 
    distance_to_tertiary_road + distance_to_city + distance_to_town + 
    water_point_population + local_population_1km + usage_capacity + 
    is_urban + water_source_clean, data = Osun_wp_sp, bw = 2597.255, 
    family = "binomial", kernel = "gaussian", adaptive = FALSE, 
    longlat = FALSE)

   Dependent (y) variable:  status
   Independent variables:  distance_to_primary_road distance_to_secondary_road distance_to_tertiary_road distance_to_city distance_to_town water_point_population local_population_1km usage_capacity is_urban water_source_clean
   Number of data points: 4756
   Used family: binomial
   ***********************************************************************
   *              Results of Generalized linear Regression               *
   ***********************************************************************

Call:
NULL

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-124.555    -1.755     1.072     1.742    34.333  

Coefficients:
                                           Estimate Std. Error z value Pr(>|z|)
Intercept                                 3.887e-01  1.124e-01   3.459 0.000543
distance_to_primary_road                 -4.642e-06  6.490e-06  -0.715 0.474422
distance_to_secondary_road               -5.143e-06  9.299e-06  -0.553 0.580230
distance_to_tertiary_road                 9.683e-05  2.073e-05   4.671 3.00e-06
distance_to_city                         -1.686e-05  3.544e-06  -4.757 1.96e-06
distance_to_town                         -1.480e-05  3.009e-06  -4.917 8.79e-07
water_point_population                   -5.097e-04  4.484e-05 -11.369  < 2e-16
local_population_1km                      3.451e-04  1.788e-05  19.295  < 2e-16
usage_capacity1000                       -6.230e-01  6.972e-02  -8.937  < 2e-16
is_urbanTRUE                             -2.971e-01  8.185e-02  -3.629 0.000284
water_source_cleanProtected Shallow Well  5.040e-01  8.574e-02   5.878 4.14e-09
water_source_cleanProtected Spring        1.288e+00  4.388e-01   2.936 0.003325
                                            
Intercept                                ***
distance_to_primary_road                    
distance_to_secondary_road                  
distance_to_tertiary_road                ***
distance_to_city                         ***
distance_to_town                         ***
water_point_population                   ***
local_population_1km                     ***
usage_capacity1000                       ***
is_urbanTRUE                             ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring       ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6534.5  on 4755  degrees of freedom
Residual deviance: 5688.0  on 4744  degrees of freedom
AIC: 5712

Number of Fisher Scoring iterations: 5


 AICc:  5712.099
 Pseudo R-square value:  0.1295351
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Fixed bandwidth: 2597.255 
   Regression points: the same locations as observations are used.
   Distance metric: A distance matrix is specified for this model calibration.

   ************Summary of Generalized GWR coefficient estimates:**********
                                                   Min.     1st Qu.      Median
   Intercept                                -8.9630e+02 -4.9805e+00  1.7599e+00
   distance_to_primary_road                 -1.9477e-02 -4.8092e-04  3.0174e-05
   distance_to_secondary_road               -1.5757e-02 -3.7583e-04  1.2438e-04
   distance_to_tertiary_road                -1.5673e-02 -4.2538e-04  7.6217e-05
   distance_to_city                         -1.8447e-02 -5.6287e-04 -1.2745e-04
   distance_to_town                         -2.2450e-02 -5.7335e-04 -1.5218e-04
   water_point_population                   -5.2830e-02 -2.2810e-03 -9.8829e-04
   local_population_1km                     -1.2757e-01  5.0016e-04  1.0647e-03
   usage_capacity1000                       -2.0846e+01 -9.7311e-01 -4.1596e-01
   is_urbanTRUE                             -1.9866e+02 -4.3054e+00 -1.6908e+00
   water_source_cleanProtected.Shallow.Well -2.0782e+01 -4.5536e-01  5.3278e-01
   water_source_cleanProtected.Spring       -5.2495e+02 -5.5983e+00  2.5500e+00
                                                3rd Qu.      Max.
   Intercept                                 1.2829e+01 1075.4234
   distance_to_primary_road                  4.8497e-04    0.0143
   distance_to_secondary_road                6.0665e-04    0.0259
   distance_to_tertiary_road                 6.7104e-04    0.0129
   distance_to_city                          2.3763e-04    0.0155
   distance_to_town                          1.9318e-04    0.0225
   water_point_population                    5.0564e-04    0.1313
   local_population_1km                      1.8177e-03    0.0392
   usage_capacity1000                        3.0334e-01    5.9492
   is_urbanTRUE                              1.2864e+00  746.9498
   water_source_cleanProtected.Shallow.Well  1.7870e+00   67.5549
   water_source_cleanProtected.Spring        6.7736e+00  331.1243
   ************************Diagnostic information*************************
   Number of data points: 4756 
   GW Deviance: 2792.323 
   AIC : 4413.603 
   AICc : 4747.217 
   Pseudo R-square value:  0.5726785 

   ***********************************************************************
   Program stops at: 2022-12-17 11:44:17 

Converting SDF into sf data.frame

To assess the performance of the gwLR, firstly, we will convert the SDF object in as data frame by using the code below:

gwr.fixed <- as.data.frame(gwlr.fixed$SDF)

Next, we will label yhat values greater or equal to 0.5 into 1 and else 0. In result of the logic comparison operation will be saved into a field called most.

gwr.fixed <- gwr.fixed %>%
  mutate(most = ifelse(
    gwr.fixed$yhat >= 0.5, T, F))
gwr.fixed$y <- as.factor(gwr.fixed$y)
gwr.fixed$most <- as.factor(gwr.fixed$most)
CM <- confusionMatrix(data=gwr.fixed$most, reference = gwr.fixed$y)
CM
Confusion Matrix and Statistics

          Reference
Prediction FALSE TRUE
     FALSE  1824  263
     TRUE    290 2379
                                          
               Accuracy : 0.8837          
                 95% CI : (0.8743, 0.8927)
    No Information Rate : 0.5555          
    P-Value [Acc > NIR] : <2e-16          
                                          
                  Kappa : 0.7642          
                                          
 Mcnemar's Test P-Value : 0.2689          
                                          
            Sensitivity : 0.8628          
            Specificity : 0.9005          
         Pos Pred Value : 0.8740          
         Neg Pred Value : 0.8913          
             Prevalence : 0.4445          
         Detection Rate : 0.3835          
   Detection Prevalence : 0.4388          
      Balanced Accuracy : 0.8816          
                                          
       'Positive' Class : FALSE           
                                          

Visualising gwLR

Osun_wp_sf_selected <- Osun_wp_sf_clean %>%
  select(c(ADM2_EN, ADM2_PCODE,
           ADM1_EN, ADM1_PCODE,
           status))
gwr_sf.fixed <- cbind(Osun_wp_sf_selected, gwr.fixed)

The code chunk below is used to create an interactive point symbol map.

tmap_mode("view")
tmap mode set to interactive viewing
prob_T <- tm_shape(Osun) +
  tm_polygons(alpha=0.1) +
tm_shape (gwr_sf.fixed) +
  tm_dots(col="yhat",
          border.col ="gray60",
          border.lwd=1) +
  tm_view(set.zoom.limits = c(8,14))
prob_T

Model Optimization